I am most interested in these two words, as I struggle to parse what itreally means to "learn" and how learning occurs. I would assert thatlearning happens within each learner's mind, depending on his or herengagement in the content. ( I am considering how much is filtered outwhile students are being exposed to the content.) I would suggest thatlearning cannot happen without students' desire to learn and that whateverany pedagogy may offer is nearly useless without student motivation tospark the learning.

> On Dec 30, 2013, at 2:41 PM, Joe Niederberger <niederberger@comcast.net>> wrote:>> More to the point -- your "proof" here isn't good enough.> In your parenthetical "reasons" you are essentially assuming the usual law> of signs. That doesn't pass muster if your goal is to prove that no other> law of signs is possible.>>> It?s a ?consistency? proof. Students in algebra do not yet have sufficient> background to justify these things deeply with formal analysis.>> If I were to guess, you confuse the emotion[1] of math with its> pedagogy[2].>> I claim that the pedagogy is universal, while the emotion is up to the> individual.>> Bob Hansen>> [1]emotion - what you like about math, which varies from student to> student.>> [2]pedagogy - how mathematical awareness builds in a student, any student.>